"The goal of the proposed research covers the following two topics:1. Theoretical foundation and investigation of different fuzzy inferences: There is a tremendous number of applications in daily life and industry where fuzzy theory is successfully applied. Those methods usually are based on a fuzzy inference. Therefore the mathematical foundation of fuzzy inferences as well as the finding of new methods which are superior to the ones applied today is an important task. Thus, this research supports the theoretical foundation of several fields of Artificial Intelligence and Software Engineering such as fuzzy control, knowledge-based systems, search engines on the web, and leads to industrial applications too.2. A study of mathematical fuzzy logics in relation to substructural logics, based on results and techniques developed recently in the study of substructural logics: Finding algebraic characterizations of different subclasses of left-continuous t-norms and residuated lattices. Further extending the geometric approach, developed in mathematical fuzzy logics by the applicant, to substructural logics. New findings at this line of the research could be very beneficial in supporting the research goals of point 1 too. A final aim is to develop a study of interrelations between algebraic methods and proof-theoretic methods in non-classical logics, in particular, in substructural logics, and in mathematical fuzzy logics in order to obtain a deeper understanding of these two disciplines."